The more I think about this with those 37's on her your loading up the entire drive line due to the amount of grip and tire weight you have. If you have a weak bushing in any of the mounts or a loose mount somewhere in the drive line the torque load would be enough to roll the components and cause it to bottom out or make metal on metal contact giving you a snapping sound. Usually a u-joint with give the tell tale "clunk" when dropping it into gear, reverse is generally worse than drive. Back in my mechanic days I've seen some bad ujoints but never anything that would give a snap when stomping on the throttle.
Now thinking this even deeper once in gear your drive line is "loaded" so any slop in a ujoint will be taken up. The only other thing I could see possibly happening is the splines on the output shaft of the tranny are toast and slipping a tooth at a time.
Does it feel like something slipping or is it tight and you just get a snapping sound?